Reminder: the two types of data  Quantitative  Observations that can be counted or measured across individuals in the population (e.g., your height, your age, your IQ score).  Categorical  Observations that fall into one of several categories (e.g., your gender, your hair color, your blood type — A, B, AB, O ). How do you figure it out? Ask:  What are the n individuals/units in the sample (of size “ n ”)?  What is being recorded about those n individuals/units?  Is that a number (  quantitative) or a statement (  categorical)?

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Binomial setting and distributions Binomial distributions are models for some categorical variables, typically representing the number of successes in a series of n independent trials. The observations must meet these requirements:  the total number of observations n is fixed in advance  each observation falls into just one of two categories: success and failure  the outcomes of all n observations are statistically independent  all n observations have the same probability of “success,” p.

Applications for binomial distributions Binomial distributions describe the possible number of times that a particular event will occur in a sequence of observations. They are used when we want to know the probability of the number of times that an occurrence takes place.  In a clinical trial, a patient’s condition may improve or not. We study the number of patients who improved, not how much better they feel.  Is a person ambitious or not? The binomial distribution describes the number of ambitious persons, and not how ambitious they are.  In quality control we assess the number of defective items in a lot of goods, irrespective of the type of defect.

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